The fourth-order algebraic diagrammatic construction scheme for the polarization propagator

Until today, perturbation-theoretical consistent algebraic diagrammatic construction (ADC) schemes for the polarization propagator had been derived and implemented up to third order. They have turned out to be versatile and reliable ab initio single-reference methods for the quantum chemical investigation of electronic transitions as well as excited-state properties. Here we present, for the first time, the derivation of consistent fourth-order ADC(4) schemes exploiting novel techniques of automated equation and code generation. The accuracies of the resulting ADC(4) excitation energies have been benchmarked against recent high-level, near exact reference data. The mean absolute error for singly and doubly excited states turns out to be smaller than 0.1 and 0.5 eV, respectively. These developments open also new avenues toward highly accurate ADC methods for electron-detached and attached states.